Middle East Journal of Applied Science & Technology (MEJAST) (Peer Reviewed & Quarterly International Journal) Volume 2, Issue 2, Pages 17-20, April-June 2019
Comparative Study of UAV Path Planning Algorithms Raina Zakir Department of Computer Engineering and Informatics, Middlesex University, Dubai, U.A.E. Article Received: 12 December 2018
Article Accepted: 17 March 2019
Article Published: 30 May 2019
ABSTRACT
This paper does a comparative study on two path planning algorithms suggested for Unmanned Aerial Vehicles (UAVs) with the intention to have least threat vector and fuel consumption during its operation. The two algorithms are based on improved Dijkstra algorithm combined with Voronoi diagram and the A* algorithm, which is suggested to have benefits over genetic and ant colony algorithms for UAV path planning. In the end, the feasibility of both the algorithms is analyzed for effectiveness. Keywords: UAV, Path Planning, Dijkstra, A* algorithm, Compare.
1. INTRODUCTION Autonomous robots, like UAVs, are widely being used for operations in hazardous environments and mission critical tasks. Some of these examples include Space exploration missions, nuclear power generations etc. One of the key areas where autonomy plays an important part is surveillance and defense where UAVs have considerable potential to solve problems associated with it, in order to reduce human casualties. With the increasing experimenting in the possibilities of incorporating UAVs in to battlefield combats, the key area of problem that is attracting research are the path planning algorithms to be used by UAVs that take in to consideration the dynamicality of threats combined with short and fuel effective routes while maintaining speed and altitude. Some path planning algorithms have been suggested in past decade to be used in UAVs where threat vector keeps on changing, some of the prominent ones include the Genetic algorithms that utilize the concept of evolution to find a satisfactory solution in path planning problems, Ant colony algorithm that uses bio-mimetic multi-point heuristic search technique to find the shortest path by the concept of ant behavior during food search in which pheromones are used guide other ants to a competent path, Dijkstra algorithm which is based on shortest path first approach to find distance between a start and target node and A* algorithm that utilizes heuristics to find shortest path using the concept of Greedy Best-First-Search. In this paper we conduct a comparison between the Improved Dijkstra algorithm with Voronoi diagramming suggested in [1] and the A* algorithm that is reported to be better than genetic and ant colony algorithms for UAV path planning in [2] as they tend converge slowly and stagnate. In the first section of this paper, we discuss the methodology proposed by [1] to solve the path planning problem for UAVs. In the second section, the methodology proposed by [2] is described followed by the comparison in the next section which then ends with a conclusion. 2. PATH PLANNING USING VORONOI DIAGRAM AND DIJKSTRA'S ALGORITHM [1] deals with using Voronoi diagram to map the distribution of threats such as radars to create a search space, that a UAV needs to avoid and then uses Dijkstra's algorithm to find the shortest and the most fuel conservative path possible using the Voronoi diagram. 17 | P a g e
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Middle East Journal of Applied Science & Technology (MEJAST) (Peer Reviewed & Quarterly International Journal) Volume 2, Issue 2, Pages 17-20, April-June 2019
An area of 8 km x 8 km is considered for the creation of the Voronoi diagram in [1], with the assumption that all the N radar threats are equal in power and in their detection radius, based on which the Voronoi representation of the threat area is created, which looks similar to the Fig 1. All the adjoining points are connected to form triangles and the perpendicular bisectors of some of the sides are used to form the polygons.
Fig. 1. Voronoi map of radar threats As long as the UAV flies on the edges of the Voronoi diagram, it remains safe. The cost of radar threat is directly proportional to the quartic of distance of UAV from the threat source and the fuel intake is directly proportional to the flight path length, which is found by Dijkstra's algorithm for optimization. The equation for the optimized path planning signifying minimum track of performance can be given as follows where i is the edge cost and fuel intake is directly proportional to the path taken at the edge:
A coefficient k is added to compromise between fuel intake and threat, with a larger value of k signifying threat being more important than amount of fuel intake, whereas a value between 0-1 suggests preference for a specific goal point. 3. PATH PLANNING USING A* ALGORITHM [2] defines path planning as finding an optimal path from a starting point, which is a node, to an end node among an area with threats in terms of low radar detectability and shortest path. For e.g., to move from a node n1 to point n2 on an edge e1 that connects both of them with the path cost as c1 the routing equation can be defined as:
Where E={e1, e2, e3, en ‌}. As the number of nodes increases, the more accurate path planning becomes assuming the UAV is flying at mid-high altitude throughout the flight without any terrain factor avoidance. [2] solves this using A start algorithm that is similar to Dijkstra's algorithm but relies on a heuristic values besides the cost of each 18 | P a g e
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Middle East Journal of Applied Science & Technology (MEJAST) (Peer Reviewed & Quarterly International Journal) Volume 2, Issue 2, Pages 17-20, April-June 2019
path. The A* algorithm stores the paths from start node on lists. The OPEN lists stores the end node of each path whereas the CLOSED list stores the other nodes, with each one of the node pointing back to its predecessor on a path as they can branch. The cost function of a node can be represented as f(n)=g(n)+h(n) Where g(n) is the path's cost from any node a to b, and h(n) is the heuristic cost, e.g. the Manhattan or Euclidean distance in evaluating the cost function. The path planning in [2] is heuristic oriented, a smaller heuristic function will search more nodes to ensure an optimal path but with more time whereas a larger list of heuristic nodes may not be able to find an optimal path but runs faster to compensate the risk. In short, as long as the heuristic is used in a way to define the cost of travelling correctly, the algorithm will follow the optimal path. Usually there is a need to set a tolerance level for optimality to improve the speed of search. As fuel cost and threat on the path is important in choosing UAV voyage, the cost function in [2] is f=g+h+ht Where g is the fuel cost and ht is used to determine if a node is a threat source. 4. THE COMPARISON Algorithms like A*, Ant Colony, Floyd's, Dijkstra's and Genetic algorithms are the most commonly used algorithms for UAV path planning [3]. The papers [1] and [2] tend to find a solution to the problem of real-time updating of threat targets while generating an optimal response and path to the target while those threats change. The papers prove the effectiveness of their solution, i.e. the effectiveness of real time path planning by showing simulations only. However, some technical comparison is needed to support the claims. One of the most important comparison is the time complexity. In case of [1], the Voronoi's computational complexity, considering Fortune's algorithm to generate one is O(nlogn) and Dijkstra's complexity can be taken as O(E log V) where E is the number of edges and V is the number vertices, when using Binary Heaps in implementation. In [2], the time complexity of the solution depends on the heuristics chosen for the A* algorithm: O(log h(x)). If we consider Manhattan distance which is used frequently in grid searches as the heuristics, theoretically we can get O(n) if each node is visited once, however realistically the complexity generally grows to O(nlogn). This makes the implementation in [2] better in terms of time complexity which in turn affects computational complexity, however [2] does not specify a clear methodology for the generation of the initial grid threat map, such as the Voronoi diagram in the case of [1]. If the heuristics in [2] turns out to be inadmissible (it overestimates the distance) for a particular threat map, the results will be non-optimal as it will reduce the accuracy compared to the Voronoi-Dijkstra approach as the approach in [2] does not only included threat as heuristic value but fuel consumption too. Another point to take in to account is the dynamicality of the threats. If threat landscape is not changing frequently and remains the same for a relatively long time than the threat map, which is the Voronoi diagram in [1] would not be changing significantly, then it might better to compute the paths of nodes using Dijkstra's algorithm based on the
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Middle East Journal of Applied Science & Technology (MEJAST) (Peer Reviewed & Quarterly International Journal) Volume 2, Issue 2, Pages 17-20, April-June 2019
cost of paths and save them for faster execution during the flying to avoid re-running the A* to find costs to all the nodes as well as the inadmissibility issue with A* algorithm in [2] that affects the radar threats and fuel. In general, Dijkstra and A* star algorithms are better in path planning problems for UAV's compared to Ant Colony algorithm which face the problem of stagnation and Genetic algorithms in which space search is slower and at the same time falling for a local minimum than a global minimum is easier [2]. 5. CONCLUSION The paper conducts a comparison between the UAV path planning algorithms suggested in [1] and [2]. The Voronoi-Dijkstra approach is suitable when the environment is less changing and best path to all nodes need to be analyzed by the UAV, like an environment where threats are constant but newly exposed to the UAV in order to be mapped while the A* approach is effective in finding distance between a start and target node as long as an admissible heuristic value is used to navigate through a threat map. REFERENCES 1. X. Chen and X. Chen, "The UAV dynamic path planning algorithm research based on Voronoi diagram," The 26th Chinese Control and Decision Conference (2014 CCDC), Changsha, 20 2. T. Chen, G. Zhang, X. Hu and J. Xiao, "Unmanned aerial vehicle route planning method based on a star algorithm," 2018 13th IEEE Conference on Industrial Electronics and Applications (ICIEA), Wuhan, 2018, pp. 1510-1514 3. Z. He and L. Zhao, "The Comparison of Four UAV Path Planning Algorithms Based on Geometry Search Algorithm," 2017 9th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), Hangzhou, 2017, pp. 33-36.
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